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Fluid dynamic applications of the discrete Boltzmann equation. (English) Zbl 0761.76001

Series on Advances in Mathematics for Applied Sciences. 3. Singapore: World Scientific. xviii, 263 p. (1991).
This book presents the development of models based on the discrete velocity Boltzmann equation. These models begin with the successful analysis of shock wave propagation and steady Couette flow given by J. Broadwell [e.g. J. Fluid Mech. 19, 401–414 (1964; Zbl 0151.41001); Phys. Fluids 7, 1243–1247 (1964; Zbl 0123.21102)]; then other discrete velocity models are proposed and remarkable mathematical results are obtained. Mathematicians have been strongly attracted by this class of models with the aim of providing useful theorems in analysis of initial and initial-boundary value problems. Contents: Chapter 1. The discrete Boltzmann equation modelling and thermodynamics. Chapter 2. Some discrete velocity models. Chapter 3. On the discrete Boltzmann equation in unbounded domains. 3.1.2. Existence of solution in the whole space. Chapter 4. Shock waves. 4.3 Existence and stability of shock waves. Chapter 5. Internal and external flows. Chapter 6. The discrete Boltzmann equation for chemically reacting gases.
Each chapter contains possible developments and open research problems for applied mathematicians and fluid-dynamicists. The book can also be used by engineers working in gas dynamics and aerospace sciences.
Reviewer: I.Grosu (Iaşi)

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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